Abstract

This paper presents an example of an actual calculation from Chapter 8 of the CPI Manual 2022. Chapter 8 in CPI Manual 2022 attempt to place most methods used by statistical agencies to quality adjust prices into a common economic framework. The economic framework is based on purchasers maximizing a linearly homogeneous utility function subject to a budget constraint on their purchases of a group of related products. This framework is far from a perfect description of reality but it captures an important empirical phenomenon: when the price of a product drops a lot, purchasers of the product buy more of it! Moreover, the theory allows us to provide a welfare interpretation for the quantity indexes which are generated by this approach. The very concept of comparing the relative quality of two related products means that we are comparing the relative usefulness or utility of the products to the purchaser. Thus it seems to be necessary to take an economic approach to the problem of quality adjustment. The theory of quality adjustment to be presented in this paper is meant to be applied at the level where subindexes are constructed at the first stage of aggregation; i.e., at what is called the elementary level of aggregation by price statisticians. Furthermore, the methods for quality adjustment to be discussed in this paper are largely aimed at the scanner data context; i.e., we will assume that the statistical agency has access to detailed price and quantity (or value) information at the product code level, either from retail outlets or from the detailed purchases of a group of similar households. Thus our focus will be on both the construction of consumer price indexes at the elementary level as well as on the companion consumer quantity indexes. The assumption of linearly homogeneous utility or valuation functions is an important restriction so one may ask: why impose it? The reason is that economic models constructed by private and public sector economists generally do not make use of disaggregated information; instead, they use the elementary indexes that are produced by national statistical agencies in their models. However, the price levels that correspond to these elementary indexes are treated as “normal” prices by applied economists; i.e., the elementary prices are not regarded as prices that are conditional on particular levels of the corresponding quantity levels. In order to construct unconditional price levels, we need to assume that the underlying aggregator or utility functions are linearly homogeneous. After summarizing the theoretical framework, this paper presents an example of hedonic index estimation using data to scanners of digital appliances in Japan.